The day in the Shire-week that came between Sterday and Monday was dedicated to the Sun, just as our own modern 'Sunday'. It derived from an older form, Sunnendei that was itself a translation of the Elvish day-name Anarya. Though the name 'Sunday' happens to be identical to a day in our modern week, the associations of the day to the Shire-hobbits would have been quite different. To them, it was an ordinary weekday, and occupied the same point in the week as Tuesday would for us.
Notes
1
Tolkien devised the names of the days in the Hobbits' week so that they were recognisable to an English-speaker, though in most cases they have a quite distinct derivation. So, for example, English 'Thursday' had its equivalent in Mersday, which ultimately derived from the Elves' 'day of the Sea' (whereas the English day takes its name from the god Thor). Sunday is one of only two exceptions (the other being Monday) where the Hobbits' day had exactly the same origins as the modern usage: the Hobbits' Sunday and Monday were named for the Sun and Moon respectively, just as in modern English.